Basic Math Examples

$\frac{2 a}{7^{3}} \div \frac{10 a^{5}}{77}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 a}{7^{3}} \cdot \frac{77}{10 a^{5}}$

Step 2

Simplify terms.

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Step 2.1

Combine.

$\frac{2 a \cdot 77}{7^{3} (10 a^{5})}$

Step 2.2

Cancel the common factor of $2$ and $10$ .

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Step 2.2.1

Factor $2$ out of $2 a \cdot 77$ .

$\frac{2 (a \cdot 77)}{7^{3} (10 a^{5})}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $7^{3} (10 a^{5})$ .

$\frac{2 (a \cdot 77)}{2 (7^{3} (5 a^{5}))}$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 (a \cdot 77)}{2 (7^{3} (5 a^{5}))}$

Step 2.2.2.3

Rewrite the expression.

$\frac{a \cdot 77}{7^{3} (5 a^{5})}$

$\frac{a \cdot 77}{7^{3} (5 a^{5})}$

$\frac{a \cdot 77}{7^{3} (5 a^{5})}$

Step 2.3

Cancel the common factor of $a$ and $a^{5}$ .

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Step 2.3.1

Factor $a$ out of $a \cdot 77$ .

$\frac{a (77)}{7^{3} (5 a^{5})}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $a$ out of $7^{3} (5 a^{5})$ .

$\frac{a (77)}{a (7^{3} (5 a^{4}))}$

Step 2.3.2.2

Cancel the common factor.

$\frac{a \cdot 77}{a (7^{3} (5 a^{4}))}$

Step 2.3.2.3

Rewrite the expression.

$\frac{77}{7^{3} (5 a^{4})}$

$\frac{77}{7^{3} (5 a^{4})}$

$\frac{77}{7^{3} (5 a^{4})}$

$\frac{77}{7^{3} (5 a^{4})}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $7$ to the power of $3$ .

$\frac{77}{343 \cdot 5 a^{4}}$

Step 3.2

Multiply $343$ by $5$ .

$\frac{77}{1715 a^{4}}$

$\frac{77}{1715 a^{4}}$

Step 4

Cancel the common factor of $77$ and $1715$ .

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Step 4.1

Factor $7$ out of $77$ .

$\frac{7 (11)}{1715 a^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $7$ out of $1715 a^{4}$ .

$\frac{7 (11)}{7 (245 a^{4})}$

Step 4.2.2

Cancel the common factor.

$\frac{7 \cdot 11}{7 (245 a^{4})}$

Step 4.2.3

Rewrite the expression.

$\frac{11}{245 a^{4}}$

$\frac{11}{245 a^{4}}$

$\frac{11}{245 a^{4}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$